Partially Inelastic Collision

Q.

de-Broglie wavelength of a body of mass 1 kg moving with velocity of 2000 m/s is

1. $0.55\times {10}^{-22}\dot{A}$

2. $3.32\times {10}^{-27}\dot{A}$

3. $1.5\times {10}^7\dot{A}$

4. None of these

Q. A body of mass $m_1$ elastically collide with another stationary body of mass $m_2$
$\begin{array}{cc}\text{Column - I}& \text{Column -II}\\ \text{(a) After the collision, velocity of second}& \left(p\right)>1\\ \text{body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(b) After the collision, the momentum}& \left(q\right)<1\\ \text{of second body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(c) After the collision, K.E. of second}& \left(r\right)=1\\ \text{body is maximum when}\frac{m_1}{m_2}\text{is}& \\ \text{(D) For elastic collision, coefficient of}& \left(s\right)=0\\ \text{restitution is}& \end{array}$

1. $a-\left(r\right)b-\left(s\right)c-\left(s\right)d-\left(r\right)$
2. $a-\left(r\right)b-\left(r\right)c-\left(s\right)d-\left(r\right)$
3. $a-\left(p\right)b-\left(q\right)c-\left(r\right)d-\left(r\right)$
4. $a-\left(p\right)b-\left(p\right)c-\left(s\right)d-\left(r\right)$

Q. Which of the following statements is incorrect regarding a partially inelastic collision?

1. Impulse of reformation is equal to the impulse of deformation.
2. Momentum remains conserved if other external forces are absent on the colliding object.
3. Total mechanical energy is not conserved during inelastic collision.
4. Coefficient of restitution lies in the range $(0<e<1)$

Q.

A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of

1. $\frac{16}{25}$

2. $\frac{2}{5}$

3. $\frac{3}{5}$

4. $\frac{9}{25}$

Q. A metal ball is moving with velocity $10\text{m/s}$ in downward direction as shown in the figure. After collision with a surface having coefficient of restitution $\left(e\right)=0.6$, it rebounds back. Find the rebound velocity. (Assume the surface remains stationary)

1. $6\text{m/s}$
2. $10\text{m/s}$
3. $60\text{m/s}$
4. $0.06\text{m/s}$

Q. A sphere of mass m moving with a constant velocity $u$ hits another stationary sphere of same mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres $\frac{v_1}{v_2}$ after collision will be

1. $\frac{1-2e}{1+2e}$
2. $\frac{1+e}{1-e}$
3. $\frac{2e+1}{2e-1}$
4. $\frac{e-1}{e+1}$

Q. In the figure shown, a block $A$ moving with velocity $20\text{m/s}$ on a horizontal surface collides with another identical block $B$, initially at rest. The coefficient of restitution is $0.5$. Neglect friction everywhere. The distance between the blocks, $5\text{sec}$ after the collision takes place is

1. $50\text{m}$
2. $125\text{m}$
3. $100\text{m}$
4. $150\text{m}$

Q. A metal ball is moving with velocity $10\text{m/s}$ in downward direction as shown in the figure. After collision with a surface having coefficient of restitution $\left(e\right)=0.6$, it rebounds back. Find the rebound velocity. (Assume the surface remains stationary)

1. $6\text{m/s}$
2. $10\text{m/s}$
3. $60\text{m/s}$
4. $0.06\text{m/s}$

Q. A ball is moving with velocity $10m/s$ in downward direction as shown in figure. After collision with fixed surface having coefficient of restitution $e=0.5$, it rebounds back with velocity $v\text{m/s}$. Find the value of $v$. (Neglect all external forces)

1. $5\text{m/s}$
2. $10\text{m/s}$
3. $8\text{m/s}$
4. $15\text{m/s}$

Q. A ball of mass $m$ moving at a speed $v$ makes a head on collision with an identical ball at rest. The kinetic energy of balls after the collision is ${\frac{3}{4}}^{\text{th}}$ of the original. If $e$ is the coefficient of restitution. Then:

1. After collision, ball which was initially at rest starts moving with velocity $\frac{1+\frac{1}{\sqrt{2}}}{2}v$
2. After collision, ball which was initially moving, has velocity $\frac{1-\frac{1}{\sqrt{2}}}{2}v$
3. $e=\frac{1}{\sqrt{2}}$
4. $e=\frac{1}{2}$

Q. A ball is moving with speed $3\text{m/s}$ in downward direction and the surface is moving with a constant speed of $2\text{m/s}$ upwards as shown in figure. After collision with the surface of coefficient of restitution $e=0.8$, the ball rebounds back with speed $v\text{m/s}$. Find the value of ${}^{\prime }{v}^{\prime }$. (Assume the surface doesn't change its velocity)

1. $3\text{m/s}$
2. $5\text{m/s}$
3. $1\text{m/s}$
4. $6\text{m/s}$

Q.

A ball of mass ${}^{\prime }{m}^{\prime }$ moving horizontally which velocity ${}^{\prime }{u}^{\prime }$ hits a wedge of mass ${}^{\prime }{M}^{\prime }$. the wedge is situated on a smooth horizontal surface. If after striking wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane. Calculate the coefficient of restitution $e$.

1. $\frac{M}{m}+ta{n}^2\theta$

2. $\frac{m}{M}+co{t}^2\theta$

3. $\frac{m}{M}+ta{n}^2\theta$

4. $\frac{M}{m}+co{t}^2\theta$

Q. In the figure shown below, a ball is moving with a velocity of $u_1=7\text{m/s}$ in downward direction towards a surface, while the surface is moving in upward direction with a constant velocity $u_2=3\text{m/s}$. If the coefficient of restitution has value of $e=0.8$ and after collision with the surface, the ball rebounds back with velocity $v\text{m/s}$, find the rebound velocity. (Neglect all external forces)

1. $5\text{m/s upward}$
2. $11\text{m/s downward}$
3. $11\text{m/s upward}$
4. $5\text{m/s downward}$

Q. In the figure shown below, a ball is moving with a velocity of $u_1=7\text{m/s}$ in downward direction towards a surface, while the surface is moving in upward direction with a constant velocity $u_2=3\text{m/s}$. If the coefficient of restitution has value of $e=0.8$ and after collision with the surface, the ball rebounds back with velocity $v\text{m/s}$, find the rebound velocity. (Neglect all external forces)

1. $5\text{m/s upward}$
2. $11\text{m/s downward}$
3. $11\text{m/s upward}$
4. $5\text{m/s downward}$

Q. Which of the following statements is incorrect regarding a partially inelastic collision?

1. Impulse of reformation is equal to the impulse of deformation.
2. Momentum remains conserved if other external forces are absent on the colliding object.
3. Total mechanical energy is not conserved during inelastic collision.
4. Coefficient of restitution lies in the range $(0<e<1)$

Q.

A ball is projected with a velocity $u$ at an elevation from a point distance d from a smooth vertical wall in a plane perpendicular to it. After rebounding from the wall, it returns to the point of projection, find the maximum distance $d$ for which the ball can return to the point of projection.

1. $\frac{e^2{u}^2}{g(1+e)}$

2. $\frac{e{u}^2}{g(1-e)}$

3. $\frac{e{u}^2}{g(1+e)}$

4. $\frac{e^2{u}^2}{g(1-e)}$